Consider the family of all circles whose centers lie on the strai | Filo

class 12

Math

Calculus

Differential Equations

568
150

Consider the family of all circles whose centers lie on the straight line y=x. If this family of circles is represented by the differential equation P y^(primeprime)+Q y^(prime)+1=0,where P ,Qare functions of x , yand y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)),then which of the following statements is (are) true?(a)P=y+x(b)P=y-x(c)P+Q=1-x+y+y^(prime)+(y^(prime))^2(d)P-Q=x+y-y^(prime)-(y^(prime))^2

568
150

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